Stabilization and regulation of nonlinear systems with applications: Robust and adaptive approach

Stabilization and output regulation are two fundamental control problems. The output regulation problem aims to design a feedback controller to achieve asymptotic tracking of a class of reference inputs and rejection of a class of disturbances in an uncertain system while maintaining the internal stability of the closed-loop system. Thus the output regulation problem is more demanding than the stabilization problem. Nevertheless, under some assumptions, the output regulation problem can be converted into a stabilization problem for a well defined augmented system and the solvability of the stabilization problem for this augmented system implies that of the output regulation problem for the original plant. Therefore, to a large extent, the study of the stabilization problem will also lay a foundation for that of the output regulation problem.;Despite the fact that significant progress has been made on the research of these two problems for nonlinear systems for over two decades, many problems are still open. In particular, so far the output regulation problem is mainly handled by robust control approach. This approach has certain fundamental limitations and cannot handle the following three cases. (1) The control direction is unknown. (2) The boundaries of system uncertainties are unknown. (3) The exosystem is not known precisely.;To handle these problems and overcome the shortcomings of the robust control approach, in this thesis, we have incorporated the adaptive control approach with the robust control approach. Both stabilization problem and output regulation problem are considered for two important classes of nonlinear systems, namely, the output feedback systems and lower triangular systems. The main contributions are summarized as follows. (1) The adaptive output regulation problem for nonlinear systems in output feedback form is addressed without knowing the control direction. The Nussbaum gain technique is incorporated with the robust control technique to handle the unknown control direction and the nonlinearly parameterized uncertainties in the system. To overcome the dilemma caused by the unknown control direction and the nonlinearly parameterized uncertainties, we have adopted a Lyapunov direct method to solve the adaptive output regulation problem. (2) The adaptive stabilization problem for nonlinear systems in lower triangular form is solved when both static and dynamic uncertainties are present and the control direction is unknown. Technically, the presence of dynamic uncertainty has made the stabilization problem more difficult than the previous work. We have managed to combine the changing supply rate technique and the Nussbaum gain technique to deal with this difficulty. The result is also applied to solve the output regulation problem for lower triangular systems with unknown control direction. (3) The adaptive output regulation problem for nonlinear systems in output feed-back form with unknown exosystem is studied. The adaptive control technique is applied to estimate the unknown parameter results from the unknown exosystem. The condition under which the parameter estimation converges to its real value is also discussed. Further, the global disturbance rejection problem for nonlinear systems in lower triangular form is solved by formulating the unknown external disturbance as a signal produced by an unknown exosystem. (4) The theoretical results have been applied to several typical control systems leading to the solution of some long standing open problems. Some exemplified applications are: (a) Global adaptive stabilization of Chua's circuit without knowing the control direction; (b) Global output synchronization of the Chua's circuit and the harmonic system; (c) Global adaptive disturbance rejection problem of the Duffing's system with all parameters unknown; (d) Global adaptive output regulation of Van der Pol oscillator with an uncertain exosystem.